Finite Group Databasebeta

← C3×#10600812 #14313453

Subgroups — C3×#10600812 #14313453

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66139C211yesmaximal, characteristic
2C2×C3×C5×#99C211yesmaximal, characteristic, complemented
3C2×C3×#3966C211yesmaximal, characteristic, complemented
4C3×#64694C212yesmaximal, complemented
5C3×#64693C212yesmaximal, complemented
6#10600812C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C2×C3×#709C411yescharacteristic, complemented
9C2×C3×C5×C22⋊C4—21no—
10C3×#4099—21no—
11C3×#4099—21no—
12C2×C3×C22⋊Dic5—21no—
13C3×#4086C411yescharacteristic, complemented
14C3×#4086C2211yescharacteristic
15C3×#4084—21no—
16C3×#4084—21no—
17C3×#4082C411yescharacteristic, complemented
18C3×#4082C2211yescharacteristic
19C3×#4072C411yescharacteristic, complemented
20C3×C5×#99—21no—
21C3×C5×#99C2212yes—
22C3×#3966—21no—
23C3×#3966C2212yes—
24C3×#2127—51nomaximal, Hall
25#66139C2×C311yescharacteristic
26C2×C5×#99C2×C311yescharacteristic, complemented
27C2×#3966C2×C311yescharacteristic, complemented
28#64694C2×C312yescomplemented
29#64693C2×C312yescomplemented
30C24×C3×C5D411yescharacteristic
31C24×C3×C5D411yescharacteristic
32C2×C3×C5×D4—41no—
33C2×C3×C5×D4—41no—
34C2×C3×C5×D4C2×C411yescharacteristic
35C2×C3×C5×D4D411yescharacteristic
36C2×C3×C5×D4D411yescharacteristic
37C2×C3×C5×D4C2311yescharacteristic
38C22×C3×C4×C5—41no—
39C22×C3×C4×C5C2×C411yescharacteristic
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5—21no—
42C2×C3×C22⋊D5—21no—
43C2×C3×C22⋊D5—21no—
44C2×C3×C22⋊D5—21no—
45C22×C3×Dic5—41no—
46C3×#709—41no—
47C3×#709—41no—
48C2×C3×D20C2×C411yescharacteristic, complemented
49C2×C3×C4×D5—21no—
50C2×C3×Dic10C2×C411yescharacteristic, complemented
51C3×C5×C22⋊C4—22no—
52C3×C5×C22⋊C4—41no—
53C3×C22⋊Dic5—21no—
54C3×C22⋊Dic5—21no—
55C3×C22⋊Dic5—21no—
56C3×C22⋊Dic5—21no—
57C3×C22⋊Dic5—21no—
58C3×C22⋊Dic5—22no—
59C3×C22⋊Dic5—41no—
60C3×C4⋊Dic5—21no—
61C3×C4×Dic5C2×C411yescharacteristic, complemented
62C3×C4×Dic5C2×C411yescharacteristic, complemented
63C3×#535—51no—
64C2×C3×#99—51no—
65C2×C3×#99D511yescharacteristic, complemented
66C3×#354—52no—
67C3×#353—52no—
68C22×C5×D4C22×C311yescharacteristic
69C2×#709C3×C411yescharacteristic, complemented
70C2×C5×C22⋊C4—21no—
71#4099—21no—
72#4099—21no—
73C2×C22⋊Dic5—21no—
74#4086C3×C411yescharacteristic, complemented
75#4086C22×C311yescharacteristic
76#4084—21no—
77#4084—21no—
78#4082C3×C411yescharacteristic, complemented
79#4082C22×C311yescharacteristic
80#4072C3×C411yescharacteristic, complemented
81C5×#99—21no—
82C5×#99C22×C312yes—
83#3966—21no—
84#3966C22×C312yes—
85#2127—51noSylow
86C23×C3×C5—21no—
87C23×C3×C5—21no—
88C23×C3×C5—21no—
89C23×C3×C5—21no—
90C23×C3×C5—81no—
91C23×C3×C5—81no—
92C23×C3×C5C22⋊C411yescharacteristic
93C23×C3×C5C22⋊C411yescharacteristic
94C23×C3×C5C22⋊C411yescharacteristic
95C23×C3×C5C2×D411yescharacteristic
96C23×C3×C5C2×D411yescharacteristic
97C22×C3×D5—21no—
98C3×C5×D4—41no—
99C3×C5×D4—41no—
100C3×C5×D4—41no—
101C3×C5×D4—41no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—42no—
105C2×C3×C4×C5—82no—
106C2×C3×C4×C5C22⋊C411yescharacteristic
107C2×C3×C4×C5C22×C411yescharacteristic
108C3×C22⋊D5—41no—
109C3×C22⋊D5—41no—
110C3×C22⋊D5—81no—
111C3×C22⋊D5—81no—
112C3×C22⋊D5—81no—
113C3×C22⋊D5—81no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5—42no—
118C2×C3×Dic5—82no—
119C3×D20—41no—
120C3×C4×D5—42no—
121C3×Dic10—41no—
122C2×C3×#41—51no—
123C22×C3×D4C2×D511yescharacteristic
124C3×#127—51no—
125C3×#127—51no—
126C3×#124—51no—
127C3×#124—51no—
128C3×#121—101no—
129C3×#121—101no—
130C3×#120—101no—
131C3×#120—101no—
132C3×#117—51no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—101no—
135C3×#99—21no—
136C3×#99—52no—
137C3×#99—101no—
138C3×#99C2×D512yes—
139C24×C5C3×D411yescharacteristic
140C24×C5C3×D411yescharacteristic
141C2×C5×D4—41no—
142C2×C5×D4—41no—
143C2×C5×D4C2×C3×C411yescharacteristic
144C2×C5×D4C3×D411yescharacteristic
145C2×C5×D4C3×D411yescharacteristic
146C2×C5×D4C23×C311yescharacteristic
147C22×C4×C5—41no—
148C22×C4×C5C2×C3×C411yescharacteristic
149C2×C22⋊D5—21no—
150C2×C22⋊D5—21no—
151C2×C22⋊D5—21no—
152C2×C22⋊D5—21no—
153C2×C22⋊D5—21no—
154C22×Dic5—41no—
155#709—41no—
156#709—41no—
157C2×D20C2×C3×C411yescharacteristic, complemented
158C2×C4×D5—21no—
159C2×Dic10C2×C3×C411yescharacteristic, complemented
160C5×C22⋊C4—22no—
161C5×C22⋊C4—41no—
162C22⋊Dic5—21no—
163C22⋊Dic5—21no—
164C22⋊Dic5—21no—
165C22⋊Dic5—21no—
166C22⋊Dic5—21no—
167C22⋊Dic5—22no—
168C22⋊Dic5—41no—
169C4⋊Dic5—21no—
170C4×Dic5C2×C3×C411yescharacteristic, complemented
171C4×Dic5C2×C3×C411yescharacteristic, complemented
172#535—51no—
173C2×#99—51no—
174C2×#99C3×D511yescharacteristic, complemented
175#354—52no—
176#353—52no—
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5—21no—
180C22×C3×C5—21no—
181C22×C3×C5—41no—
182C22×C3×C5—41no—
183C22×C3×C5—41no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5—42no—
187C22×C3×C5—42no—
188C22×C3×C5—81no—
189C22×C3×C5—81no—
190C22×C3×C5#9911yescharacteristic
191C22×C3×C5#9911yescharacteristic
192C22×C3×C5C2×C22⋊C411yescharacteristic
193C2×C3×D5—41no—
194C2×C3×D5—41no—
195C2×C3×D5—41no—
196C3×C4×C5—21no—
197C3×C4×C5—21no—
198C3×C4×C5—82no—
199C3×Dic5—41no—
200C3×Dic5—41no—
201C3×Dic5—41no—
202C3×Dic5—82no—
203C24×C3D2011yescharacteristic
204C24×C3C22⋊D511yescharacteristic
205C3×#41—201no—
206C3×#41—201no—
207C2×C3×Q8—51no—
208C2×C3×D4—41no—
209C2×C3×D4—41no—
210C2×C3×D4—51no—
211C2×C3×D4—101no—
212C2×C3×D4—101no—
213C2×C3×D4—101no—
214C2×C3×D4—101no—
215C2×C3×D4—101no—
216C2×C3×D4C4×D511yescharacteristic
217C2×C3×D4D2011yescharacteristic
218C2×C3×D4C22⋊D511yescharacteristic
219C2×C3×D4C22×D511yescharacteristic
220C22×C3×C4—41no—
221C22×C3×C4—101no—
222C22×C3×C4—201no—
223C22×C3×C4C4×D511yescharacteristic
224C3×C4⋊C4—101no—
225C3×C22⋊C4—22no—
226C3×C22⋊C4—41no—
227C3×C22⋊C4—101no—
228C3×C22⋊C4—101no—
229C3×C22⋊C4—101no—
230C3×C22⋊C4—101no—
231C3×C22⋊C4—101no—
232C3×C22⋊C4—102no—
233C3×C22⋊C4—201no—
234C3×C42—51no—
235C3×C42—51no—
236C23×C5—21no—
237C23×C5—21no—
238C23×C5—21no—
239C23×C5—21no—
240C23×C5—81no—
241C23×C5—81no—
242C23×C5C3×C22⋊C411yescharacteristic
243C23×C5C3×C22⋊C411yescharacteristic
244C23×C5C3×C22⋊C411yescharacteristic
245C23×C5C2×C3×D411yescharacteristic
246C23×C5C2×C3×D411yescharacteristic
247C22×D5—21no—
248C5×D4—41no—
249C5×D4—41no—
250C5×D4—41no—
251C5×D4—41no—
252C2×C4×C5—21no—
253C2×C4×C5—21no—
254C2×C4×C5—42no—
255C2×C4×C5—82no—
256C2×C4×C5C3×C22⋊C411yescharacteristic
257C2×C4×C5C22×C3×C411yescharacteristic
258C22⋊D5—41no—
259C22⋊D5—41no—
260C22⋊D5—81no—
261C22⋊D5—81no—
262C22⋊D5—81no—
263C22⋊D5—81no—
264C2×Dic5—21no—
265C2×Dic5—21no—
266C2×Dic5—21no—
267C2×Dic5—42no—
268C2×Dic5—82no—
269D20—41no—
270C4×D5—42no—
271Dic10—41no—
272C2×#41—51no—
273C22×D4C2×C3×D511yescharacteristic
274#127—51no—
275#127—51no—
276#124—51no—
277#124—51no—
278#121—101no—
279#121—101no—
280#120—101no—
281#120—101no—
282#117—51no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—101no—
285#99—21no—
286#99—52no—
287#99—101no—
288#99C2×C3×D512yes—
289C2×C3×C5—21no—
290C2×C3×C5—21no—
291C2×C3×C5—21no—
292C2×C3×C5—41no—
293C2×C3×C5—41no—
294C2×C3×C5—41no—
295C2×C3×C5—41no—
296C2×C3×C5C2×#9911yescharacteristic
297C3×D5—81no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—81no—
303C23×C3—81no—
304C23×C3—101no—
305C23×C3#68511yescharacteristic
306C23×C3#68511yescharacteristic
307C23×C3#68511yescharacteristic
308C23×C3C2×D2011yescharacteristic
309C23×C3C2×C22⋊D511yescharacteristic
310C3×Q8—201no—
311C3×D4—41no—
312C3×D4—41no—
313C3×D4—41no—
314C3×D4—41no—
315C3×D4—201no—
316C3×D4—201no—
317C3×D4—201no—
318C3×D4—401no—
319C3×D4—401no—
320C3×D4—401no—
321C3×D4—401no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—42no—
325C2×C3×C4—82no—
326C2×C3×C4—101no—
327C2×C3×C4—101no—
328C2×C3×C4—101no—
329C2×C3×C4—202no—
330C2×C3×C4—202no—
331C2×C3×C4—402no—
332C2×C3×C4#68511yescharacteristic
333C2×C3×C4C2×C4×D511yescharacteristic
334C22×C5—21no—
335C22×C5—21no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5—41no—
339C22×C5—41no—
340C22×C5—41no—
341C22×C5—41no—
342C22×C5—41no—
343C22×C5—42no—
344C22×C5—42no—
345C22×C5—81no—
346C22×C5—81no—
347C22×C5C3×#9911yescharacteristic
348C22×C5C3×#9911yescharacteristic
349C22×C5C2×C3×C22⋊C411yescharacteristic
350C2×D5—41no—
351C2×D5—41no—
352C2×D5—41no—
353C4×C5—21no—
354C4×C5—21no—
355C4×C5—82no—
356Dic5—41no—
357Dic5—41no—
358Dic5—41no—
359Dic5—82no—
360C24C3×D2011yescharacteristic
361C24C3×C22⋊D511yescharacteristic
362#41—201no—
363#41—201no—
364C2×Q8—51no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—51no—
368C2×D4—101no—
369C2×D4—101no—
370C2×D4—101no—
371C2×D4—101no—
372C2×D4—101no—
373C2×D4C3×C4×D511yescharacteristic
374C2×D4C3×D2011yescharacteristic
375C2×D4C3×C22⋊D511yescharacteristic
376C2×D4C22×C3×D511yescharacteristic
377C22×C4—41no—
378C22×C4—101no—
379C22×C4—201no—
380C22×C4C3×C4×D511yescharacteristic
381C4⋊C4—101no—
382C22⋊C4—22no—
383C22⋊C4—41no—
384C22⋊C4—101no—
385C22⋊C4—101no—
386C22⋊C4—101no—
387C22⋊C4—101no—
388C22⋊C4—101no—
389C22⋊C4—102no—
390C22⋊C4—201no—
391C42—51no—
392C42—51no—
393C3×C5#212711yescharacteristic, complemented, Hall
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—81no—
406C22×C3—81no—
407C22×C3—201no—
408C22×C3—201no—
409C22×C3—201no—
410C22×C3#393811yescharacteristic
411C22×C3#393811yescharacteristic
412C22×C3C2×#68511yescharacteristic
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—82no—
416C3×C4—201no—
417C3×C4—201no—
418C3×C4—201no—
419C3×C4—402no—
420C2×C5—21no—
421C2×C5—21no—
422C2×C5—21no—
423C2×C5—41no—
424C2×C5—41no—
425C2×C5—41no—
426C2×C5—41no—
427C2×C5C2×C3×#9911yescharacteristic
428D5—81no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—81no—
434C23—81no—
435C23—101no—
436C23C3×#68511yescharacteristic
437C23C3×#68511yescharacteristic
438C23C3×#68511yescharacteristic
439C23C2×C3×D2011yescharacteristic
440C23C2×C3×C22⋊D511yescharacteristic
441Q8—201no—
442D4—41no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—201no—
447D4—201no—
448D4—201no—
449D4—401no—
450D4—401no—
451D4—401no—
452D4—401no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—42no—
456C2×C4—82no—
457C2×C4—101no—
458C2×C4—101no—
459C2×C4—101no—
460C2×C4—202no—
461C2×C4—202no—
462C2×C4—402no—
463C2×C4C3×#68511yescharacteristic
464C2×C4C2×C3×C4×D511yescharacteristic
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—41no—
469C2×C3—41no—
470C2×C3—41no—
471C2×C3—41no—
472C2×C3—401no—
473C2×C3C2×#393811yescharacteristic
474C5C3×#212711yescharacteristic, complemented, Sylow
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—42no—
485C22—42no—
486C22—81no—
487C22—81no—
488C22—201no—
489C22—201no—
490C22—201no—
491C22C3×#393811yescharacteristic
492C22C3×#393811yescharacteristic
493C22C2×C3×#68511yescharacteristic
494C4—21no—
495C4—21no—
496C4—82no—
497C4—201no—
498C4—201no—
499C4—201no—
500C4—402no—
501C3#1060081211yescharacteristic, direct product factor, Sylow
502C2—21no—
503C2—21no—
504C2—21no—
505C2—41no—
506C2—41no—
507C2—41no—
508C2—41no—
509C2—401no—
510C2C2×C3×#393811yescharacteristic
subgroupG/H
centerC2×C3C2×#3938
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×D4C22×C3×D5
FittingC2×C3×C5×#99C2
socleC2×C3×C5C2×#99
prime radicalC3×#66139C2
cosocleC2×C5×D4C23×C3
hypercenterC2×C3×#99D5
hypocenterC5C3×#2127
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C22×C3×D4 ◁ C2×C3×#99

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×C5×#99C2semidirect
3. C2×C3×#3966C2semidirect
4. C3×#64694C2semidirect
5. C3×#64693C2semidirect
6. #10600812C3direct (N × H)
8. C2×C3×#709C4semidirect
13. C3×#4086C4semidirect
17. C3×#4082C4semidirect
19. C3×#4072C4semidirect
26. C2×C5×#99C2×C3semidirect
27. C2×#3966C2×C3semidirect
28. #64694C2×C3semidirect
29. #64693C2×C3semidirect
48. C2×C3×D20C2×C4semidirect
50. C2×C3×Dic10C2×C4semidirect
61. C3×C4×Dic5C2×C4semidirect
62. C3×C4×Dic5C2×C4semidirect
65. C2×C3×#99D5semidirect
69. C2×#709C3×C4semidirect
74. #4086C3×C4semidirect
78. #4082C3×C4semidirect
80. #4072C3×C4semidirect
157. C2×D20C2×C3×C4semidirect
159. C2×Dic10C2×C3×C4semidirect
170. C4×Dic5C2×C3×C4semidirect
171. C4×Dic5C2×C3×C4semidirect
174. C2×#99C3×D5semidirect
393. C3×C5#2127semidirect
474. C5C3×#2127semidirect
501. C3#10600812direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#661392
C2×C3×C5×#992
C2×C3×#39662
C3×#646942
C3×#646932
#106008123
C3×#21275